I don't know much about old English and Irish music, and nothing at all about the others, but till someone knowledgeable shows up . . .
The Celts had a great many instruments, including the terrifying carnyx and various other horns, all of which could produce notes from the harmonic series. If an expert player had been able to reach the higher partials of the series, s/he might have been able to play at least part of a scale. That scale would have included the deliciously out-of-tune notes you can hear in the Prologue and Epilogue of Britten's Serenade for Tenor, Horn and Strings.
There are claims that the crwth, which is depicted in the ninth century Bible of Charles the Bald, may have been a staple of Welsh musicians a thousand years earlier. But the few survivors had lost their strings when they were unearthed, and even if they hadn't they would have lost their tunings of course. The same is true of the Iron Age lyre (c.300 BC) found on the Isle of Skye, and the clarsach.
Even the many bone and wood whistles, pipes and pan pipes that have been found are so badly decayed that their tunings are imprecise.
There was always singing of course. The Old English epic poem Beowulf (written down around the year 1000 AD but describing events in Scandinavia in the 6th century) was possibly sung. If it was sung there is evidence it was sung to only a handful of notes, or rather, a small number of melodic formulae. [It's interesting then to speculate on whether these melodic formulae owe anything to the nomoi (melodic formulae) developed in the seventh century BC by Terpander of Lesbos, which were used to accompany recitations of the Homeric epics.]
There may be faint echoes of the bardic tradition and its scales in Welsh and Irish music, though nowadays the tunings will accord with equal temperament.
You ask, 'If nothing is known, what is likely?' We probably had various pentatonic scales, but how they sounded is a matter for conjecture. Remember that a pentatonic scale in, say, Indonesia is a quite different beast - and often a much sweeter, more expressive one - than the one you can play on a piano.
For a bit more on pentatonic scales may I refer you to my answer to a vaguely similar question here? (Why are the 4th and 7th scale degrees removed from the major scale to make the Pentatonic scale?)
Time signatures? No idea. We always walked on two feet, so I daresay two beats were always popular. And because we built Stonehenge we probably went, "PULL - two - three. PULL - two - three", introducing 3/4 to an audience already bored with 2/4! And perhaps we had a form of singing without a strict metre, in the manner of the ancient clarsach music and the more recent pibroch.